Just for the heck of it I calculated the distances between the ballot boxes to downtown location and what would be a good location for a W. Seattle one.
Ballard to Downtown 6.0 mi
Magnuson Park 7.7 mi
In W. Seattle I thought either the Highpoint or Southwest Branch would be good locations.
Highpoint 5.7 mi
Southwest 7.7 mi
Both locations are fairly central in W. Seattle and have parking available.